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Qu$$stion $2$

$C_1=500+5\mathrm{.}3P_1+0\mathrm{.}004P_1^2$

$C_2=400+5\mathrm{.}5P_2+0\mathrm{.}006P_2^2$

$C_3=200+5\mathrm{.}8P_3+0\mathrm{.}009P_3^2$

Where $P_1,P_2,$ and $P_3$ are in MW$.$ The total power demand is $P_D=1200MW.$

Neglecting line losses and generator limits$.$

Determine the optimal scheduling of generation $P_2$